Original scientific paper

Smooth cohomology of \(C^*-algebras\)

Masoud Amini ; Department of Mathematics, Tarbiat Modares University, P.O Box 14 115-175, Tehran, Iran
Ahmad Shirinkalam ; Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

We define a notion of smooth cohomology for \( C^* \)-algebras which admit a faithful trace. We show that if \( \A\subseteq B(\h) \) is a \( C^* \)-algebra with a faithful normal trace \( \tau \) on the ultra-weak closure \( \bar{A} \) of \( \mathcal{A} \), and \( X \) is a normal dual operatorial \( \bar{A}\)-bimodule, then the first smooth cohomology \( \mathcal{H}^1_{s}(\mathcal{A},X) \) of \( \mathcal{A} \) is equal to \( \mathcal{H}^1(\mathcal{A},X_{\tau})\), where \( X_{\tau} \) is a closed submodule of \( X \) consisting of smooth elements.

Keywords

smooth cohomology; group action; equivariant bimodule; faithful trace

Hrčak ID:

252598

URI

https://hrcak.srce.hr/252598

Publication date:

10.3.2021.

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